Find the quadratic polynomial whose zeroes are 3+ √5 and 3_√5

1.	Find the quadratic polynomial whose zeroes are 3+ √5 and 3_√5
Answer» This also seems like you didn\'t learn chapter 4 in a better way.{tex}\\large{Question: \\space Zeroes=3+\\sqrt5 \\space and \\space 3-\\sqrt 5,\\space find\\space the \\space quadratic\\space equation?}{/tex}{tex}\\large Solution:{/tex}\t{tex}\\large {For\\space any\\space quadratic\\space equation,\\space x^2+x\\times(\\alpha+\\beta)+(\\alpha\\times\\beta)=0\\space }{/tex}{tex}\\large {Here,\\space let\\space\\space\\alpha=3+\\sqrt5 \\space\\space\\space\\space,\\space\\space\\space\\space\\beta=3-\\sqrt5.\\space }{/tex}{tex}\\large {Thus,\\space\\space\\space\\alpha+\\beta=3+\\sqrt5 +3-\\sqrt5 = 6\\space\\space\\space\\space,\\space\\space and\\space\\space\\alpha\\times\\beta=(3+\\sqrt5)(3-\\sqrt5)=3^2-\\sqrt5 ^2=9-5=4.\\space }{/tex}{tex}\\large {\\therefore\\space x^2+x\\times(\\alpha+\\beta)+(\\alpha\\times\\beta)=0\\space }\\\\\\large {\\implies\\space x^2+x\\times(6)+(4)=0\\space }\\\\\\large {\\implies\\boxed{\\space x^2+6x+4=0}\\space }\\\\{/tex}\tNow after seeing this, don\'t you think this is a very very simple thing to do.

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